Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}8x-9y &= -4 \\ 4x+3y &= -8\end{align*}$
Begin by moving the $x$ -term in the second equation to the right side of the equation. $3y = -4x-8$ Divide both sides by $3$ to isolate $y$ $y = {-\dfrac{4}{3}x - \dfrac{8}{3}}$ Substitute this expression for $y$ in the first equation. $8x-9({-\dfrac{4}{3}x - \dfrac{8}{3}}) = -4$ $8x + 12x + 24 = -4$ Simplify by combining terms, then solve for $x$ $20x + 24 = -4$ $20x = -28$ $x = -\dfrac{7}{5}$ Substitute $-\dfrac{7}{5}$ for $x$ back into the top equation. $8( -\dfrac{7}{5})-9y = -4$ $-\dfrac{56}{5}-9y = -4$ $-9y = \dfrac{36}{5}$ $y = -\dfrac{4}{5}$ The solution is $\enspace x = -\dfrac{7}{5}, \enspace y = -\dfrac{4}{5}$.